Neural Network Based Modeling and Model Predictive Control for Reduction in Diesel Emissions

The paper illustrates the process and steps in the development of a neural network-based economic Model Predictive Control (MPC) strategy for reducing diesel engine feed gas emissions. This MPC controller performs fuel limiting and modifies intake manifold pressure and exhaust gas recirculation (EGR) rate set-points to the inner loop air path controller to reduce engine-out oxides of nitrogen (NOx) and Soot emissions. We examine two Recurrent Neural Network (RNN) options for a control-oriented emissions model which are based on a multi-layer perception (MLP) architecture and a long short-term memory (LSTM) architecture. These RNN models are trained for use as prediction models in MPC. Both models are defined in input-output form, assuming that measurements/estimates of current values of NOx and Soot are available. We discuss and compare their training using PyTorch. The formulation of economic MPC is detailed, including the definition of the cost function and soft constraints. Approaches based on interior point methods and sequential quadratic programming for the numerical solution of the underlying optimization problem in MPC are summarized. Closed-loop simulations of the control system and the plant model in GT-Power demonstrate that both methods have the capability to shape engine-out emissions effectively by adjusting weights and constraints in the economic MPC formulation. The solutions with MLP-based and LSTM-based RNN are then compared based on several aspects such as model complexity, training time, tuning, closed-loop performance, and execution time. The closed-loop performance in terms of cumulative NOx and Soot exceeding soft constraints is compared based on Pareto fronts for the respective controller options. Methods to reduce online runtime are also studied. The results highlight the tradeoff between NOx and Soot emissions, and that better open-loop prediction accuracy achieved with the LSTM Neural Network model compared to the MLP model does not necessarily translate into better closed-loop performance when used as a part of the MPC controller.